The invention relates to a fuel injection apparatus of the type such as is shown in German laid-open application No. 1,807,965. In this apparatus, the fuel delivery line, which has a constant pressure of approximately 1000 bar, is in continuous direct communication with the pressure chamber. It is disadvantageous, however, that if the valves are not tight, the fuel is continually injected because it is at a constant high pressure and there is a correspondingly high leakage flow. As a result, incomplete combustion takes place, causing smoking and sooting. In addition, the oil film can be washed off by the fuel which is injected in excess amounts and hence unconsumed, which can lead to piston corrosion and/or seizing and to significant damage.